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OPTIMIZE THE AUTOPILOT SECTION OF AIRCRAFT USING EVOLUTIONARY ALGORITHMS Nguyen M.H. (Socialist Republic of Vietnam) Email: [email protected]
Nguyen Minh Hong - PhD in Automatic Control, DEPUTY DIRECTOR OF THE AIRCRAFT CONTROL CENTER OF CONTROL SYSTEMS AND AIRCRAFT, LE QUYDON TECHNICAL UNIVERSITY, HA NOI, SOCIAL REPUBLIC OF VIETNAM
Abstract: flight control system plays an important role in the quality of aircraft guidance. The task of this system is to ensure the stability of the system and to make sure that the aircraft obeys correctly according to the guidance commands. This paper proposes a method of using evolutionary algorithms to design autopilot for non-minimum phase aircrafts. To make the paper more relevant to reality, the paper takes into account the dynamics of the steering engine during simulation. Cost function used for evolutionary algorithms takes into account the influence of the characteristic parameters on the quality of the autopilot system, such as system response speed, overcorrection, setting errors, etc. Simulations will be made with two dynamics models of the aircraft. Simulation results show that the evolutionary algorithms may be used to design coefficients for other traditional autopilots.
Keywords: autopilot, aircraft, inertia measurement, flight control system.
ОПТИМИЗАЦИЯ АВТОПИЛОТА ЛЕТАТЕЛЬНОГО АППАРАТА ПРИ ИСПОЛЬЗОВАНИИ ЭВОЛЮЦИОННЫХ АЛГОРИТМОВ Нгуен М.Х. (Социалистическая Республика Вьетнам)
Нгуен Минь Хонг - кандидат технических наук автоматического управления, заместитель директора, Научно-исследовательский центр развития системы управления летательных аппаратов, Вьетнамский государственный технический университет им. Ле Куй Дона, г. Ханой, Социалистическая Республика Вьетнам
Аннотация: система управления полетом играет важную роль в качестве наведения летательного аппарата. Задача этой системы заключается в обеспечении стабильности системы и уверенности в том, что летательный аппарат выполняет указания командования. В этой работе предлагается способ использования эволюционных алгоритмов для разработки автопилота для не-минимально-фазовых летательных аппаратов. При моделировании учитывается динамика автопилота. Функция затрат, используемая для эволюционного алгоритма, учитывает влияние характерных параметров на качество системы автопилот, например скорость отклика системы, перерегулирование, ошибки регулирования и т.д. Моделирование будет производиться с двумя динамическими моделями летательного аппарата. Результаты моделирования показывают, что эволюционные алгоритмы могут применяться для разработки коэффициентов другого традиционного автопилота.
Ключевые слова: автопилот, летательный аппарат, измерение инерции, система управления полетом.
1. Introduction
The effect of destroying the target of aircraft mainly depends on the guidance and control system (GNC). Therefore, a study that discusses ways of destroying the target most effectively via autopilot and flight control systems is interesting for many researchers [5], [8], [10, 11], [12], [18], [20], [22], [23], [24], [25], [27].
Gain-scheduling is one of the effective control methods for nonlinear systems and systems with variable parameters [18], [22]. This method has also been used to design the autopilot systems for vehicles like aircrafts [20]. This method takes a lot of time, which is a disadvantage; it has been proven many times. Some solutions have also been suggested by [5], [8], [10], [11], [12]. The author of [15] suggested a method to use fuzzy logic to design the gain-scheduling autopilot system.
An autopilot system must meet minimum requirements on stability and responsiveness maintenance. In addition, the errors in the aircraft system must be minimal. For non-minimum phase systems, it is required to set upper and lower limits of sub-standard overcorrection. Evolutionary algorithms adapt autopilot coefficients automatically. This article uses the cost function taking into account the characteristic parameters of autopilot system quality, such as high response speed and minimal errors. Evolutionary optimization methods will be compared to highlight the effectiveness of the proposed method. The superiority of this method over traditional methods will be reflected in the simulation results. 2. Elements of the flight control system Elements of flight control system shown on the Figure 1 [12].
Fig. 1. Primary elements of the flight control system
On the Fig. 1, inertia measurement (IMU) is used to measure the angular velocity and translation acceleration of aircraft. The algorithm navigation transforms the measurements of IMU into different coordinate systems. The output of the guidance law sections is the guidance commands, which are taken to autopilot along with the output of the navigation section to make sure that the aircrafts will follow the desired commands. Steering engine's task is to convert the command control signals into the physical control signals. Finally, the aircraft will follow this physical control signals. Mission of the flight control system is to ensure that the aircraft will successfully perform the desired mission.
2.1. Aircraft dynamics
Aircraft dynamics are described through equations of movement. Fig. 2 shows the flight process in the pitch plane of the aircraft. Here y is the flight path angle, a is the angle of attack, d is the pitch angle, Az is the normal acceleration vector.
InertiaI reference
Fig. 2. Position of the aircraft in the pitch plane
The equations describing the angle relationship are given below:
a = 8 — y a = 8 — y (1)
8 = (2)
Here J is the moment of inertia, M(a,S) is the moment of putting on the aircraft. Speed of flight path angle y is determined by the following equation:
Aycos(a) Ay
with V, magnitude of the velocity vector and Az is determined by the following equation:
FJa.S)
(4)
Here m is the mass of the aircraft and Fz(a,S) is the normal force act on the aircraft. By replacing (3) and (4) into (1) and combine with (2), we get the following two nonlinear differential equations:
a = 8
Fz(a,8)
8 =
M(a,S)
(5)
mV ' J
In fact, the movement of the aircraft is represented in three-dimensional space as shown in the figure 3 with the meaning of the parameters shown in Table 1.
Fig. 3. Dynamics of the aircraft in three-dimensional space
Parameters Meaning
a Angle of attack
ß Angle of sideslip
aT Total angle of sideslip
<Pa Roll angle
Vm Velocity of the aircraft
V Velocity of rotation angle of the aircraft's vertical axis
<7 Velocity of rotation angle of the aircraft in pitch plane
r Velocity of rotation angle of the aircraft in horizon plane
xb>yb>zb Coordinates of the aircraft on three coordinate system axes
Assuming that there is no centrifuge torque, the equations for translational movement control
and rotational movement are represented by equations (6) and (7) respectively:
iF F \
a = cos2 a (-Z&- — p tan B + q sec2 a--— tana — r tana tan B )
xmu r r mu rj
fF F \ ^ '
B = cos2 B (-2^-- r sec2 B + p tana--—tan B + q tan a tan B |
^ ^ \mu ^ F mu r v r j
Mxb Iz ~ ly
h h
Myb
ly ly
Mzb ly
qr
pr (7)
pq
h h
Accelerants that are perpendicular to the aircraft are determined in the aircraft coordinate system as follows:
Az=^, Ay=^ (8)
m y m
Here forces (Fxb,Fyb,Fzb) and moments(Mxfc,Myfc,Mzfc) are determined in the aircraft coordinate system. Force and moment vectors are the functions of the state variables and three control inputs. For example, force vector Fzb is denoted as follows:
Fzb = fist. p. p. q, r, <V sq, Sr) (9)
By linearizing the equations (6) and (8) nearby the working points of the system, the invariantstate space model is given in (10) with three inputs and five outputs as follows:
x = [a /3 p q r]T
(x = Ax + Bu ) _ rr r r I7"
n t
[ y = Cx + DW 1 u = [8p8q8r] (10)
ly = [Ay Az p q r]
Where Sp, Sq and Sr is the control input in the pitch, yaw and roll channels, respectively.
2.2. Autopilot
Autopilot is a system with inputs as guidance commands and measurements from IMU to calculate control commands. Almost all digital signals and calculations for the autopilot are calculated by computers.
2.3. Steering engine
Steering engine is used to transform the control commands into physical movements, such as rotational movement of the aircraft's wings. The dynamics of the steering engine is modeled by the second-order transfer function with latency t as follows: 8(s) (xil
—— =---e"TS (11)
Sc(s) s2 + 2 $aa>as + w2
3. Design method of autopilot
This section introduces a new structure for the acceleration control system. In addition, evolutionary algorithms will also be introduced in this section. 3.1. Acceleration control system
Fig. 4. Block diagram of acceleration control system
The proposed structure of acceleration control system is shown on Fig. 4. Here the aircraft velocity on the pitch channel q and acceleration^ are measured by IMU. According to Fig. 4, the error between acceleration command and real acceleration is used as a PI controller input to control aircraft velocity on pitch channel. In this paper, coefficients of autopilot are adjusted by meta-heuristic algorithms.
Fig. 5 shows the Step response of the system with parameters such as setting time ts, rising time tr, time until the first peak tp, t is the time constant and Mp is the maximum overcorrection. In this paper the combination of these features will be used to achieve the best results in seeking space. Equation (12) describes the cost function used in this paper.
/ = (Wits) + (w2Mp) + (w3Mu) + (w4 J t. e2(t) dtj + (w5 J|u(t)|dt) (12)
Here wi, w2, w3, w4 and w5 are the weights. These weights are chosen by the designer to balance the role of each element in the cost function. e(t) is the error signal between the reference input and the output, u(t) is the control signal and Mu is the maximum sub-standard.
Thus, the cost function takes into account the effects of the specific parameters of the system simultaneously. Consequently, evolutionary algorithms can optimize all features of the system on every iteration.
Fig. 5. Step response of the non-minimum phase system
3.2. Evolutionary algorithms
This section introduces five evolutionary algorithms used for design of autopilot for aircraft [19].
- Genetic Algorithm (GA): GA is the earliest and most common evolutionary algorithm. It is been used in many different areas [7].
- Particle Swarm Optimization (PSO): PSO was suggested by [17].
- Artificial Bee Colony (ABC): ABC was introduced by Karaboga [13] and has been successfully applied in technical problems [14], [15], [16].
- Independent Component Analysis ICA: ICA was introduced by Atashpaz and Lucas (2007) for optimization problems [1].
- Cuckoo optimization algorithm (COA): COA is inspired by the cuckoo bird who lays eggs in the nest of other birds of different species. The results show that this is a very good evolutionary algorithm for solving optimal problems [3].
4. Simulation results
This section provides simulation with two different aircraft models. The first aircraft model is short-range aircraft using conventional diagram. Aircraft dynamics can be linear in the vicinity of nominal working point (Attack angle reaches 10o and speed reaches 3 Mach). Dynamic description functions are linearized in the vicinity of nominal working point for pitch channel as follows: Az(s) _ 0.2038s2 - 239.7687 5(s) ~ s2 + 1.12s+ 87.176 q(s) -131s- 131 (13)
5 is) s2 + 1.12s+ 87.176
In addition, we assume that the dynamics of steering engine is represented approximately by the second-order transfer function with the following parameters: , and
. The parameters of the optimization methods are shown in Table 2. All evolutionary algorithms use the cost function (12) with the following limits of coefficients (seeking space) for the first model:
-10 <Kt< 10; —5<Kp<5,—l<Kq<l (14)
Optimization methods Parameters
GA Hybrid probability: 0.1 Mutation probability: 0.9
PSO C1: 1.5; C2: 1.5
ABC Amount of food: 50
ICA Evolution speed: 0.3 f = 0.02
COA Number of groups: 5, Minimum number of eggs: 2, Maximum number of eggs: 5 Number of Cuckoo that can live at the same time: 150
During the simulation, all algorithms have population sizes of 100 and the number of loops of 50. After optimizing the coefficients of the autopilot for the five evolutionary algorithms with the parameters given in Table 2, we get five graphs describing the cost function for the five algorithms as shown in Fig. 6.
s —*-1-1-1-1-1-1-1-1-1-
_I_I_I_I_I_I_I_I_I_
D S 10 IS 2D 2S 30 3S « « M
It er at Ian
Fig. 6. Compare the costfunction values during implementation of five evolutionary algorithms for the first
model of aircraft
Fig. 6 shows that optimization algorithm COA achieves the fastest and best quality solution. The value of characteristic parameters for five step responses, coefficients of autopilot and cost function received using the five evolutionary algorithms are shown in Table 3.
ICA GA ABC POS COA
Raising Time (s) 0.1240 0.1485 0.1979 0.1041 0.1164
Setting time (s) 0.2414 0.2735 0.3612 0.2114 0.2306
Overcorrection (%) 0 0 0 0 0
Sub-standard (%) 9.9341 7.6523 6.1698 11.5611 10.5503
Peak 0.9996 0.9988 0.9995 0.9995 0.9996
Time Constant (s) 0.136 0.124 0.181 0.156 0.131
Kp -0.5040 -0.3856 -0.3089 -0.5886 -0.5361
K, -3.3498 -2.8460 -2.5330 -3.6226 -3.4556
Kq -0.1403 -0.1230 -0.1257 -0.1468 -0.1430
Minimum cost function 4.0118 4.0467 4.2299 3.9395 3.9154
The simulation results show the superiority of COA compared to the others. With the coefficients received when COA are applied, step response of autopilot is shown in Fig. 7.
Fig. 7. Step response and the control signal in correspondence to the COA for the first model
In the second simulation, this paper provides a survey with aircraft dynamic model presented by Horton [18], [20], [24], [25], [27]. The related transfer functions are given below: XO) 433.5s2 + 722.3s- 2060000
8{s)
s2 + 5.314s+ 278.2 -872.8s- 3011
<7 (s) =_
5(s) ~ s2 + 5.314s + 278.2
(15)
In this case, the dynamic parameters of the steering engine are , and
. Cost functions and parameters of evolutionary algorithms are similar to the first simulation (equation (12) and table 2). The upper and lower limits of the autopilot coefficients (seeking space) for the second simulation are as follows:
-0.01 <Ki< 0.01, -0.1 <Kq< 0.1, Kp = 0 (16)
With all the algorithms, the population size is 100 and maximum number of loops is 50. Then the results when implementing evolutionary algorithms and characteristics of step response obtained are corresponding to coefficients of autopilot for each of the evolutionary algorithms shown in Table 4.
Table 4. Implementation results of evolutionary algorithms for the second model
ICA GA ABC POS COA
Raising Time (s) 0.1771 0.1774 0.1772 0.1771 0.1769
Setting Time (s) 0.3268 0.3272 0.3268 0.3266 0.3263
Overcorrection(%) 0.1296 0.1250 0.1288 0.1304 0.1333
Sub-standard (%) 0.4240 0.4240 0.4240 0.4239 0.4239
Peak 1.0008 1.0008 1.0008 1.0008 1.0008
Time Constant (s) 0.206 0.207 0.206 0.206 0.206
Kp 0 0 0 0 0
K, -8.3913E-4 -8.3931E-4 -8.3915E-4 -8.3904E-4 -8.3895E-4
Kq -0.0159 -0.0159 -0.0158 -0.0159 -0.0158
Minimum cost function 2.2418 2.2421 2.2416 2.2416 2.2412
The results show that this method is very effective for determining the autopilot coefficients. The time constant of COA is approximately 0.206 s. Fig. 8 shows the step response of the system with the control signal corresponding to the autopilot coefficients received when COA is applied.
■iil_i_i_i_i_i_i_i_i_i_
0 <1_L li H)J (L* LI Hi LJ OJ <Li 1
Time
Fig. 8. Step response and the control signal corresponding to the autopilot coefficients received by applying
the COA algorithm
5. Conclusion
In this paper, a new method for determining the autopilot coefficients for non-minimum phase aircraft was evaluated. With the proposed method, autopilot is developed with lower cost and better quality compared to using other evolutionary algorithms. The results obtained when performing simulations with two different models show that evolutionary algorithms have a superior preponderance advantage when calibrating and determining the autopilot coefficients compared to traditional methods. When implementing various evolutionary algorithms, such as GA, PSO, ABC, ICA and COA, COA shows its superiority, compared to
other algorithms. During the simulation, the paper also takes into account the dynamics of steering engine to improve the reality of the simulation results.
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WASTEWATER TREATMENT OF FLINT HYDROFLUORIC ACIDS Shirinova D.B. (Republic of Azerbaijan) Email: [email protected]
Shirinova Durdana Bakir gizi - Аssociate Рго/essor, DEPARTMENT OF PETROCHEMICAL TECHNOLOGY AND INDUSTRIAL ECOLOGY, FACULTY OF CHEMICAL TECHNOLOGY, AZERBAIJAN STATE UNIVERSITY OF OIL AND INDUSTRY, BAKU, AZERBAIJAN REPUBLIC
Abstract: we studied the possibility of wastewater treatment of kremneftoristovodorodnoj acid. Conducted a retrospective analysis of methods of wastewater treatment of flint hydrofluoric acid using different filter materials. It was determined that the wastewater from flint hydrofluoric acid can be carried out using as a filter material mixture, contact waste klinoptilolit mass of sulfuric acid productions and cement. Thus contact weight is production with drawal Found that achieved a relatively high amount of wastewater treatment flint hydrofluoric acid.
Keywords: sewage, purification, hexafluorosilicic acid, clinoptilolite, contact mass.
ОЧИСТКА СТОЧНЫХ ВОД ОТ КРЕМНЕФТОРИСТОВОДОРОДНОЙ
КИСЛОТЫ Ширинова Д.Б. (Азербайджанская Республика)
Ширинова Дурдана Бакир кызы - доцент, кафедра нефтехимической технологии и промышленной экологии, химико-технологический факультет, Азербайджанский государственный университет нефти и промышленности, г. Баку, Азербайджанская Республика
Аннотация: изучена возможность очистки сточных вод от кремнефтористоводородной кислоты. Проведен ретроспективный анализ методов очистки сточных вод от кремнефтористоводородной кислоты с применением различных фильтрующих веществ. Определено, что очистку сточных вод от кремнефтористоводородной кислоты можно осуществить с использованием в качестве фильтрующего материала смеси клиноптилолита, отработанной контактной массы сернокислотных производств и цемента. При этом контактная масса является отходом производства.
